Question

If $S_1$ and $S_2$ are respectively the sets of local minimum and local maximum points of the function, $f\left(x\right)=9x^4+12x^3-36x^2+25,x\in R,$ then:

• A. $S_1=\{-2,0\};S_2=\left\{1\right\}$
• B. $S_1=\{-2,1\};S_2=\left\{0\right\}$
• C. $S_1=\{-1\};S_2=\{0,2\}$
• D. $S_1=\{-2\};S_2=\{0,1\}$

Answer 1

The correct option is B $S_1=\{-2,1\};S_2=\left\{0\right\}$

$f\left(x\right)=9x^4+12x^3-36x^2+25$
$f^{\prime }\left(x\right)=36x^3+36x^2-72x$
$f^{\prime }\left(x\right)=36x(x^2+x-2)$
$f^{\prime }\left(x\right)=36x(x+2)(x-1)$

Sign of $f^{\prime }\left(x\right)$

$S_1=\{-2,1\}$
$S_2=\left\{0\right\}$